How Much of a Rope Can Hang Over a Table Without Sliding?

[frog210293]

Homework Statement

a) If the co efficent of static friction between a table and a uniform massive rope is Us, what fraction of the rope can hang over the edge of the table without the rope sliding?

Homework Equations

F=mg

The Attempt at a Solution

The largest fraction of the rope able to overhang would be 1/2?, how would you go about proving that mathematically?

The force on the rope hanging down would be F=m*9.81

where to go from here?

 

[ehild]

Make the free-body diagram for both pieces of the rope (hanging and resting on the table). Find the condition when it just starts to slide.

ehild